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How many 7 letter words can be constructed using 26 letters

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How many 7 letter words can be constructed using 26 letters [#permalink] New post 12 Apr 2006, 19:09
How many 7 letter words can be constructed using 26 letters of the alphabet if each word contains 3 vowels (repetitions allowed)

a) (21^4)*(5^3)
b) (21^4)*(5^3)*7!
c) {(21^4)*(5^3)*7!}/4!*3!
d) 21C4*5C3*7!
e) None of these
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Re: P&C - 7 letter word [#permalink] New post 12 Apr 2006, 20:28
chillpill wrote:
How many 7 letter words can be constructed using 26 letters of the alphabet if each word contains 3 vowels (repetitions allowed)

a) (21^4)*(5^3)
b) (21^4)*(5^3)*7!
c) {(21^4)*(5^3)*7!}/4!*3!
d) 21C4*5C3*7!
e) None of these


total = 26
vowels (a, e, i, o, and u) = 5
consonants = 21

no of ways 3 vowels can be selected from 5 vowels = 5c3
no of ways 4 (7-3) consonants can be selected from 21 consonants= 21c4
no of ways 7 words can be arranged = 7!
so multiply all then its

(D) 21C4*5C3*7!
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Re: P&C - 7 letter word [#permalink] New post 12 Apr 2006, 20:39
Professor wrote:
chillpill wrote:
How many 7 letter words can be constructed using 26 letters of the alphabet if each word contains 3 vowels (repetitions allowed)

a) (21^4)*(5^3)
b) (21^4)*(5^3)*7!
c) {(21^4)*(5^3)*7!}/4!*3!
d) 21C4*5C3*7!
e) None of these


total = 26
vowels (a, e, i, o, and u) = 5
consonants = 21

no of ways 3 vowels can be selected from 5 vowels = 5c3
no of ways 4 (7-3) consonants can be selected from 21 consonants= 21c4
no of ways 7 words can be arranged = 7!
so multiply all then its

(D) 21C4*5C3*7!

10x you are really an El Professore)))
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 [#permalink] New post 12 Apr 2006, 23:29
Think that since repetitions are allowed it should be B)
Four consonants can be selected each in 21 ways, 3 vowels in 5 ways each and they can have 7! orderings. Now if the words have to be different then we come to A)
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 [#permalink] New post 13 Apr 2006, 02:17
The 7 letter word can be

V V V C C C C which can be arranged in 7! ways.

Each V can be any of the 5 vowels.
Each C can be any of the 21 Consonants - since repetition is allowed.

(5*5*5 * 21*21*21*21 ) * 7!

Ans = B
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 [#permalink] New post 13 Apr 2006, 06:01
I thought the words do have to be different. This would give us A, correct?
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 [#permalink] New post 13 Apr 2006, 14:25
BG is right...D is correct
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 [#permalink] New post 13 Apr 2006, 16:56
BG wrote:
Think that since repetitions are allowed it should be B)
Four consonants can be selected each in 21 ways, 3 vowels in 5 ways each and they can have 7! orderings. Now if the words have to be different then we come to A)


you are right. i didnot cinsider "repititon." :evil: :evil: :twisted: :twisted:
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 [#permalink] New post 14 Apr 2006, 07:17
YES! I care about repetition

(5*5*5 * 21*21*21*21) * 7!
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 [#permalink] New post 14 Apr 2006, 19:56
Professor wrote:
BG wrote:
Think that since repetitions are allowed it should be B)
Four consonants can be selected each in 21 ways, 3 vowels in 5 ways each and they can have 7! orderings. Now if the words have to be different then we come to A)


you are right. i didnot cinsider "repititon." :evil: :evil: :twisted: :twisted:


But even if you consider repetition, A should not be the answer. I think C is the correct Answer.

- Vipin
  [#permalink] 14 Apr 2006, 19:56
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How many 7 letter words can be constructed using 26 letters

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